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1. Projectile with air resistance: A projectile of mass m is fired vertically upwards from ground with velocity vo. It experiences air resistance, which we model as a drag force magnitude kv (k is the linear drag coefficient and is a constant) that acts on the projectil the direction opposite to its velocity. (a) Set up the differential equation for the velocity of the projectile as a function of v(t). Write down the initial conditions. (b) Solve the differential equation in (b) for v(t). (c) Integrate v(t) over time to find the height of the projectile versus time, y(t). Note at t = 0, y = 0 since the projectile starts from the ground.

1. Projectile with air resistance: A projectile of mass m is fired vertically upwards from ground with velocity vo. It experiences air resistance, which we model as a drag force magnitude kv (k is the linear drag coefficient and is a constant) that acts on the projectil the direction opposite to its velocity. (a) Set up the differential equation for the velocity of the projectile as a function of v(t). Write down the initial conditions. (b) Solve the differential equation in (b) for v(t). (c) Integrate v(t) over time to find the height of the projectile versus time, y(t). Note at t = 0, y = 0 since the projectile starts from the ground.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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1. Projectile with air resistance: A projectile of mass m is fired vertically upwards from the ground with velocity vo. It experiences air resistance, which we model as a drag force with magnitude kv (k is the linear drag coefficient and is a constant) that acts on the projectile in the direction opposite to its velocity. (a) Set up the differential equation for the velocity of the projectile as a function of time v(t). Write down the initial conditions. (b) Solve the differential equation in (b) for v(t). (c) Integrate v(t) over time to find the height of the projectile versus time, y(t). Note that at t= 0, y = 0 since the projectile starts from the ground. (d) Plot y(t) versus t for a few different values of k to see the effect of air resistance on the trajectory (large k means larger air resistance). Note: In reality, the air drag force is a quadratic function Cu², where C is a constant, but this makes the problem harder to solve. Try it if you are adventurous!
Transcribed Image Text:1. Projectile with air resistance: A projectile of mass m is fired vertically upwards from the ground with velocity vo. It experiences air resistance, which we model as a drag force with magnitude kv (k is the linear drag coefficient and is a constant) that acts on the projectile in the direction opposite to its velocity. (a) Set up the differential equation for the velocity of the projectile as a function of time v(t). Write down the initial conditions. (b) Solve the differential equation in (b) for v(t). (c) Integrate v(t) over time to find the height of the projectile versus time, y(t). Note that at t= 0, y = 0 since the projectile starts from the ground. (d) Plot y(t) versus t for a few different values of k to see the effect of air resistance on the trajectory (large k means larger air resistance). Note: In reality, the air drag force is a quadratic function Cu², where C is a constant, but this makes the problem harder to solve. Try it if you are adventurous!
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